Points to Ponder

The distance an object travels along its path between two points is usually larger than the straight-line distance between those points (the magnitude of displacement). Displacement depends only on where you start and end; path length depends on the route taken. They are equal only if the object never reverses direction — otherwise, path length is always greater.

Because of point 1, average speed (total path length divided by time) is always greater than or equal to the magnitude of average velocity (displacement divided by time). They match only when the path length equals the magnitude of displacement — that is, when motion is in a straight line without turning back.

The vector equations $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ and $\mathbf{s} = \mathbf{u}t + \frac{1}{2}\mathbf{a}t^{2}$ are independent of any coordinate system. You can always choose any two perpendicular axes to break them into components, but the vector form itself does not assume a particular set of axes.

The standard kinematic equations for constant acceleration do not apply to uniform circular motion. In uniform circular motion, the magnitude of acceleration is constant, but its direction keeps changing — so the acceleration is not constant in the vector sense.

When an object has two velocities $\mathbf{v}_1$ and $\mathbf{v}_2$, its resultant velocity is $\mathbf{v} = \mathbf{v}_1 + \mathbf{v}_2$. Do not confuse this with relative velocity: the velocity of object 1 relative to object 2 is $\mathbf{v}_{12} = \mathbf{v}_1 - \mathbf{v}_2$, where both $\mathbf{v}_1$ and $\mathbf{v}_2$ are measured from the same reference frame. …